Micellar Shape Transformation Induced by Decanol - American

Study by Small-Angle X-ray Scattering (SAXS) ... curves show an increase in the maximum dimension of the spheroidal micelles with Md ratios of up to 0...
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6102

Langmuir 2000, 16, 6102-6109

Micellar Shape Transformation Induced by Decanol: A Study by Small-Angle X-ray Scattering (SAXS) Cilaˆine Veroˆnica Teixeira, Rosangela Itri,* and Lia Queiroz do Amaral Instituto de Fı´sica da USP, C.P. 66318, Sa˜ o Paulo, SP 05315-970, Brazil Received September 28, 1999. In Final Form: April 20, 2000

Sodium dodecyl (lauryl) sulfate (SLS)/water/decanol systems at a fixed water/SLS molar ratio of 144.0 (10 wt % SLS in water) and varying decanol/SLS molar ratios (Md) were studied through small-angle X-ray scattering (SAXS). Results from the distance and electron distribution functions retrieved from the SAXS curves show an increase in the maximum dimension of the spheroidal micelles with Md ratios of up to 0.18. At Md ) 0.20, the micelle symmetries change from spherical to cylindrical, with an anisotropy (ratio between the longest and the shortest dimension) close to 1.8, according to bending energy requirements. Micellar aggregates self-assemble into cylinder-like particles with Md ratios of up to 0.40, where a cylinder f disk shape transformation is observed. The cylinder f disk transition occurs at nearly the same Md as that of the nematic cylindrical f nematic discotic liquid-crystalline phase transition in more concentrated systems. The transformation also agrees with bending energy requirements for the polar/apolar interface in mixed micelles. Furthermore, the amount of bound water per polar head remains the same in both the more diluted and the more concentrated systems.

I. Introduction The anionic amphiphile sodium lauryl sulfate (SLS) has been extensively studied in micellar isotropic solutions as well as in liquid-crystalline phases. The SLS/water binary system has hexagonal (HR) and lamellar (LR) phases1 and some intermediate phases with long-range positional order,2 and the nematic domain is obtained in the ternary system by decanol addition.3-5 An isotropic (I) f hexagonal (HR) f nematic cylindrical (Nc) phase sequence was recently studied6-8 in systems containing water/SLS molar ratios (Mw) of 45.2 and 39.4 and varying decanol/SLS molar ratios (Md). It has also been observed6 that the decanol addition in the SLS/water system initially promotes a micellar growth greater than that of the SLS/water binary system via SLS addition. The Nc f nematic discotic (Nd) phase transition in the SLS/water system induced by decanol addition has also been studied,4,9-11 and it was shown that this transition is accompanied by a micellar shape evolution from spherocylinder to disk.11 The partitioning of cosurfactant in mixed micelles has been analyzed by Gelbart,12 who showed that the cosurfactant inserts preferentially into the body, rather than into the caps of spherocylinder aggregates, to minimize the electrostatic interaction * Corresponding author. E-mail: [email protected]. (1) Ekwall, P. In Advances in Liquid Crystals; Academic: London, 1975; Vol. 1, p 1. (2) Ke´kicheff, P.; Cabane, B. J. Phys. (Paris) 1987, 48, 1571. (3) Amaral, L. Q.; Helene, M. E. M.; Bittencourt, D. R.; Itri, R. J. Phys. Chem., 1987, 91, 5949. (4) Amaral, L. Q.; Helene, M. E. M. J. Phys. Chem. 1988, 92, 6094. (5) Quist, P. O.; Halle, B.; Furo´, I. J. Chem. Phys. 1991, 95, 6945. (6) Itri, R.; Amaral, L. Q. Phys. Rev. E 1993, 47, 2551. Erratum in Itri, R.; Amaral, L. Q. Phys. Rev. E 1998, 58, 1173. (7) Teixeira, C. V.; Itri, R.; Amaral, L. Q. Langmuir 1999, 15, 936. (8) Santin Filho, O.; Itri, R.; Amaral, L. Q. J. Phys. Chem. B 2000, 104, 959. (9) Amaral, L. Q. Liq. Cryst. 1990, 7, 877. (10) Quist, P. O. Liq. Cryst. 1995, 18, 623. (11) Amaral, L. Q.; Santin Filho, O.; Taddei, G.; Vila-Romeu, N. Langmuir 1997, 13, 5016. (12) Gelbart, W. M.; McMullen, W. E.; Masters, A.; Ben-Shaul, A. Langmuir 1985, 1, 101.

between the polar heads. Preferential partitioning of decanol in the lower curvature zones of the micelles has also been experimentally observed.13 It is clear that the decanol has a strong influence on the phase transitions, although its entire mechanism is not completely understood yet. Decanol promotes a nematic domain with long-range orientational order between two long-range positional order phases (hexagonal and lamellar), and it also changes the micellar form at the Nc f Nd transition. The I f H f Nc phase sequence has been7,8 examined with statistics mechanical theories of selfaggregation with a predefined symmetry of the aggregate. On the other hand, the Nc f Nd transition as a function of Md could be explained by Amaral et al.11 in terms of an elastic bending theory for a single mixed micelle. The phenomenological theory of Helfrich14 gives the bending energy of bilayered membranes as a function of the principal and spontaneous curvatures of the membrane interfaces via the elastic constants (bending rigidity and elastic modulus of Gaussian curvature). Hyde has developed a semiempirical model15 where the same bending energy is expressed in terms of the actual surfactant parameter p (related to the curvature of the micellar interface) and the spontaneous molecular surfactant parameter p0, introduced by Israelachvili16 (p0 ) v/al, where v, l, and a are, respectively, the hydrophobic chain volume, the effective chain length, and the polar head areasthe area available per hydrophilic group at the hydrocarbon/water interface). The bending energy is proportional to (p - p0)2, integrated over the micellar surface. Hyde’s model has the advantage of being easily applicable to the case of surfactant monolayers, even with the radii of curvature equal to the chain lengths. It has (13) Hendrikx, Y.; Charvolin, J.; Rawiso, M. J. Colloid Interface Sci. 1984, 100, 597. (14) Helfrich, W. Z. Naturforsch., Teil C 1973, 28, 693. (15) Hyde, S. T. J. Phys. Chem. 1989, 93, 1458. (16) Israelachvili, J. N.; Mitchell, D. J.; Ninham, B. W. J. Chem. Soc., Faraday Trans. 2 1976, 72, 1525.

10.1021/la9912848 CCC: $19.00 © 2000 American Chemical Society Published on Web 06/30/2000

Micellar Shape Transformation Induced by Decanol

been explicitly discussed17 that Helfrich’s formulation is more suitable for the case of spontaneous planar surfaces and that Hyde’s model accounts more naturally for the case of spontaneously curved interfaces. Hyde’s model was the basis for the mixed micelle model of Amaral et al.11 that explains the change in micelle form from cylinder to planar at the Ncf Nd phase transition (with an increase in Md) as a consequence of the different p0 values of the amphiphile and decanol molecules. Such a model accounts well for the observed Nc f Nd transitions for three diferent systems, but it has the obvious drawback of taking into account only intra-aggregate and not interaggregate interactions. It is therefore important to verify whether such a model holds also in the isotropic phase, and this is the aim of the present paper. We study the influence of decanol on the SLS/water system in the I phase by varying Md at 10 wt % SLS/ water, which corresponds to a Mw of 144.0, kept fixed. Although interactions of charged systems exist even at low surfactant volume fractions, it has been previously shown6,18,19 that, up to this concentration, the maximum of the SLS intermicellar interference function falls almost exactly in the region of the minimum of the intramicellar factor in the small-angle X-ray scattering (SAXS) curve. As a consequence, the SAXS curve presents a peak which is dominated by the detailed form of the micelle. Interference effects start to become important in the intramicellar peak only at 15 wt % SLS.6,19 Accordingly, the isotropic curves are analyzed through the distance distribution and the electron density distribution functions, which allow us to evaluate both the particle maximum dimension and the particle symmetry (sphere-like, cylinder-like, or lamella-like), as will be described in the following section. Similar studies were performed on D2O/C12E5 mixtures and microemulsions to study changes of form induced by temperature20 and mixtures of oppositely charged surfactants.21 The methodology has the advantage of being model-free. II. Materials and Methods Materials. Commercial Merck SLS (99% purity), deionized bidistilled water, and BDH decanol were used. The samples consisted of 10 wt % SLS in water, and decanol was added from Md ) 0 to Md ) 0.45. The solutions were homogenized through agitation and centrifugation and conditioned in sealed capillaries of 1 mm i.d. The Md range was chosen in such a way that we could cover all the Md values at which the liquid-crystalline phase transitions were observed for the system containing 26.25 wt % SLS/water4,6,7,11 in comparing the already known results with the decanol effect in the isotropic phase. The samples were studied by SAXS at room temperature (22 ( 1 °C). The scattering curves were obtained by means of a smallangle goniometer, assembled on a Rigaku generator, with line beam transmission geometry and CuKR radiation. The value of the scattered intensity was corrected by subtracting the value of the parasitic scattering, which consists of the value of the measured intensity without sample, multiplied by the value of the sample attenuation. Any electronic noise was also subtracted. The experimental points for q < 0.04 Å-1 (q ) scattering vector ) 4π/λ sin θ, where λ is the wavelength and 2θ is the scattering angle) were abandoned because of the strong influence of the parasitic scattering. (17) Figden, A.; Hyde, S. T.; Lundberg, G. J. Chem. Soc., Fadaray Trans. 1991, 87, 949. (18) Itri, R.; Amaral, L. Q. J. Phys. Chem. 1991, 95, 423. (19) Itri, R.; Amaral, L. Q. J. Appl. Crystallogr. 1994, 27, 20. (20) Iampietro, D. J.; Brasher, L. L.; Kaler, E. W.; Stradner, A.; Glatter, O. J. Phys. Chem. B 1998, 102, 3105. (21) Strey, R.; Glatter, O.; Schubert, K. V.; Kaler, E. W. J. Chem. Phys. 1996, 105, 1175.

Langmuir, Vol. 16, No. 15, 2000 6103 Analysis Method. The SAXS curves were analyzed through indirect Fourier transformation by using the method developed by O. Glatter (ITP),22,23 as used in refs 18 and 19, followed by a deconvolution technique (Decon), also developed by Glatter.24 The Fourier transformation yields the pair distance distribution p(r), which gives information about the particle maximum dimension Dmax (p(r) ) 0 for r ) 0 and r g Dmax). For a particle of arbitrary shape and scattering density contrast F(r) (electron density for X-rays), p(r) is given by24-26

pd(r) ) rd-1Fd(r)

(1)

where d is 1, 2, or 3 for the scattering density at a normal distance from the lamella plane, from the cylinder axis, or from the center of the sphere, respectively. Accordingly, for a chosen particle geometry, the scattering density profile F(r) is calculated by a deconvolution technique. In particular, the program Decon generates the F(r) function correlated with the p j (r) pair distance distribution function that best agrees with the p(r) function generated by ITP. If the chosen particle symmetry deviates from the real one, the p j (r) function is a poor approximation of the input p(r) function.24 Thus, the particle geometry is inferred by comparing the distance distribution obtained from the scattering data to that calculated theoretically for a given symmetry and scattering density profile. From the micellar maximum dimension values, Dmax, obtained from the p(r) curves, it is possible to calculate the paraffinic anisotropy, ν, of spheroidal micellar aggregates as the ratio between the longest and the smallest axes of the paraffinic medium in the micelle

ν)

Dmax/2 - 4.6 Rparef

(2)

with Rparef ) 16.7(1 - f) + 14.2f, where f is the decanol molar fraction and 16.7 and 14.2 Å correspond to the lengths of fully extended dodecyl and decyl paraffin chains, respectively.27 In eq 2, a value of 4.6 Å28 for the polar shell thickness was used. Such a procedure was adopted to compare the results with those in the previous work.6 Generally, it is possible to obtain the size of cylindrical and lamellar particles when they present anisotropy values greater than 2.5 (up to about 10) so that p(r) decays linearly from the particle cross-section size to its maximum distance.29 Nevertheless, in the present work, only Dmax values smaller than 78 Å can be evaluated, due to our experimental resolution (Dmax e π/qmin, with qmin ) 0.04 Å-1). Thus, in our case, p(r) does not show a linear behavior at r values larger than the length of the particle cross section, and hence, it was not possible to evaluate the cylinder-like and disk-like micelle maximum dimensions. However, we do recognize changes in the particle symmetry through comparison between p(r) and p j (r). From ν, it is also possible to calculate the volume of the micellar polar shell (Vpol) and, consequently, the number of water molecules per polar head (NH) in the micelles

Vpol ) n j SLSvSO4 + n j SLS(1 - R)vNa + n j DeOHvj DeOH + NHn j vH2O (3) where Vpol ) 4/3πν(Rpol3 - Rpar3) is the volume of the micelle polar shell (Rpar is the paraffin size and Rpol is the total size of j DeOH the micelle), n j SLS is the SLS average aggregation number, n ) Mdn j SLS is the decanol average aggregation number, n j)n j SLS +n j DeOH ) n j SLS(1 + Md) is the total aggregation number (surfactant + cosurfactant), vSO4 ) 60.6 Å3 is the SO4 volume, vNa ) 31 Å3 (22) Glatter, O. Acta Phys. Austr. 1977, 47, 83. (23) Glatter, O. J. Appl. Crystallogr. 1977, 10, 415. (24) Glatter, O. J. Appl. Crystallogr. 1981, 14, 101. (25) Glatter, O.; Hainisch, B. J. Appl. Crystallogr. 1984, 17, 435. (26) Glatter, O. J. Appl. Crystallogr. 1980, 13, 577. (27) Tanford, C. J. Phys. Chem. 1972, 76, 3020. (28) Stigter, D. J. Phys. Chem. 1964, 68, 3603. (29) Glatter, O. J. Appl. Crystallogr. 1979, 12, 166.

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Figure 1. 10 wt % SLS/water, with Md ) 0 and 0.18. Left side: 0, distance distribution function p(r) obtained by ITP; s, p j (r) obtained by Decon for spherical symmetry. Right side: 0, experimental scattering data; s, scattering curves generated by ITP from the corresponding p(r) functions. Table 1. Maximum Dimension of Particles Obtained from the p(r) Functions and Rpar Values Obtained from the Electron Density Distribution G(r) Mapsa

is the Na volume, vDeOH ) 21 Å3 is the OH volume at the decanol polar head, vH2O ) 30 Å3 is the volume of the water molecule, and R is the ionization coefficient.

III. Results Figure 1 exhibits the p(r) functions (open squares) obtained from the SAXS curves for the samples composed of 10 wt % SLS/water with Md ) 0 and 0.18, along with the p j (r) functions (thick lines) generated by Decon via supposing spherical symmetry. The corresponding experimental data fitted with the theoretical scattering curves generated by ITP are shown on the right side of Figure 1. As we can see from the figure, there is good agreement between the observed and the modeled scattering curves, as well as between p(r) and p j (r) functions. Similar results were obtained for the samples with Md ) 0.10 and 0.14 under the same quality of fitting. Such good agreement indicates that the micelles must have a spherical symmetry for the studied Md values. From the p(r) functions, the values of Dmax were obtained and are exhibited in Table 1. The data in Table 1 indicate an increase in the maximum dimension of the particles as Md increases to 0.18. We will return to this point in the discussion of the results. j (r) function As far as the result for Md ) 0.20, the p starts to deviate within evaluated uncertainties from the input p(r) function at the second peak region, as seen in Figure 2. Such a mismatch is more pronounced for increasing Md values (Figure 2 at Md ) 0.33), indicating a symmetry change. Thus, a micellar cylindrical symmetry was postulated, leading to a better agreement between the p j c(r) and pc(r) functions shown in Figure 2. The values

Md

Dmax ((1) (Å)b

Rpar ((2) (Å)c

symmetry

0 0.10 0.14 0.18

56 55 61 61

16 16 16 16

sph sph sph sph

Md

Dmax - cross-section length ((1) (Å)

Rpar ((2) (Å)

symmetry

0.20 0.33 0.38

46 46 46

13 13 13

cyl cyl cyl

Md

Dmax - thickness ((1) (Å)

Rpar ((2) (Å)

symmetry

0.40 0.45

41 41

8 9

lam lam

a Symmetries: sph ) spherical; cyl ) cylindrical; lam ) lamellar. For Dmax, the error bars were estimated from the graphics by dividing Dmax by the number of points in the p(r) functions and taking half of this smaller unit as the error. c For Rpar, the error bars were estimated by taking half of the width of a step in the F(r) profile.

b

obtained for the cylinder-like micelle cross sections are given in Table 1. Going further in the analysis for Md ) 0.38 and 0.40, we have also performed the analysis of planar symmetry, since a cylinder-like to disk-like transformation had been previously observed at Md ) 0.38 in the Nc f Nd phase transition.4,11 For Md ) 0.38, we observe that for cylindrical symmetry, the p j c(r) function still fits very well the pc(r) function, whereas for the planar symmetry, there is a

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Figure 2. 10 wt % SLS/water, with Md ) 0.20 and 0.33: 0, distance distribution function p(r) obtained by ITP; s, p j (r) obtained by Decon for spherical and cylindrical symmetries.

great deviation between p j t(r) and pt(r) functions in the position of the second peak (Figure 3). On the other hand, for Md ) 0.40, there is slight deviation between Fj(r) and Fc(r) in the position of the second peak. The agreement between p j t(r) and pt(r) functions improves for lamellar symmetry at Md ) 0.40 (Figure 3). The result for lamellar symmetry is more successful than for cylindrical symmetry, although the result for cylindrical symmetry at Md ) 0.40 was not too bad. For Md ) 0.45 (Figure 3), the lamellar symmetry is better than the cylindrical. Thus, at Md ) 0.38, cylindrical micelles are more compatible with the experimental data, whereas disk-like micellar aggregates are formed at Md ) 0.40 and 0.45. The values of the thickness of the disk-like micelles are shown in Table 1. The corresponding electron density distribution functions are shown in Figure 4. The number of steps (7) was chosen so as to have the best resolution of the electron density levels. Such levels (given by the program in arbitrary units) were normalized by considering two levels of electron density: FCH3 ) 0.167 e/Å3 (corresponding to CH3) and Fwater ) 0.327 e/Å3 (corresponding to water, the solvent). Since the paraffinic electron density (Fpar) is lower than the water electron density (Fwater) and the polar shell electron density (Fpol) is higher than the water electron density (Fwater), one can estimate the paraffinic region extension (Rpar) to be the point where F(r) intersects with Fwater. Following this procedure, we obtained the Rpar values shown in Table 1. Notice that Rpar values decrease as the micelles pass from spherical to cylindrical symmetry as well as when they pass from cylindrical to lamellar symmetry. For geometric reasons, the diameter of the cylinder cross section is expected to be only slightly smaller than the length of two extended surfactant chains, whereas

the thickness of the lamella can be up to 30% smaller than that length.30 In fact, there is a decrease of Rpar accompanying the change of micellar symmetry. The Rpar values obtained for spherical symmetry are compatible with the expected Rparef ) 16.7 Å for Md ) 0 and Rpar ) 16.25 Å for Md ) 0.18. For cylindrical symmetry, the Rpar values are slightly smaller than Rparef (expected to be 15.9 Å for Md ) 0.33). The lamellar symmetry’s Rpar, 30% smaller than 15.7 Å (for Md ) 0.40) and 15.6 Å (for Md ) 0.45), should be both approximately 11.0 Å, but we obtained values of 9 ( 2 and 8 ( 2 Å. These differences are within the estimated uncertainties. It can also be observed in Figure 4 that the polar electron density decreases as decanol is added, although the symmetry is maintained. This is a consequence of the fact that the SLS polar heads are farther apart due to the presence of decanol between them. Nevertheless, when the symmetry is changed from sphere to cylinder or from cylinder to lamella, the electron density increases, because the available volume per polar head is greater for sphere than for cylinders and greater for cylinders than for lamellae. Besides the quality of the fitting of the p j (r) and p(r) functions, the micelle shape evolution can also be interpreted through the ratio between the first and second peak heights of p(r). In Figure 1, we observe that for Md ) 0, the second peak is higher than the first one, and for Md ) 0.18, the first peak is higher. These ratios are kept for the cylindrical symmetry and become much higher for lamellar symmetry (Md ) 0.40 and 0.45). Figure 5a shows the superposition of the homogeneous sphere p(r) and the 10 wt % SLS/water (without decanol) curve. It can be (30) Tiddy, G. J. T. Phys. Rep. 1980, 57, 1.

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Figure 3. 10 wt % SLS/water, with Md ) 0.38, 0.40, and 0.45: 0, distance distribution function p(r) obtained by ITP; s, p j (r) obtained by Decon for spherical, cylindrical, and lamellar symmetries.

clearly seen that the second of the two peaks has greater intensity. Then, observing the graph of the homogeneous cylinder, we notice that the peak is moved toward smaller r values so that the first peak of the inhomogeneous curve becomes higher than the second one (Figure 5b). Finally, the homogeneous lamellar distance distribution function is such that the first peak of the inhomogeneous pt(r) is even higher (Figure 5c) than in the previous, homogeneous case. The height inversion at Md ) 0.18 means that at this concentration, the system is very close to the spheroid f j c(r) cylinder transition. For Md ) 0.20 the fitting of the p and pc(r) functions is not as good as for Md ) 0.33 and 0.38. On the other hand, the p j (r) and p(r) fit is not as bad as it is for higher concentrations. The same can be said about the fitting of cylinder and lamella for Md ) 0.40. Even if the changes of symmetry were occurring sharply as a function of Md, they appear softer in the analysis of p(r) because the changes of symmetry are followed by an increase of length (and also an increase of micelle volume and a decrease of the particle number density).11 The changes of symmetry become evident in p(r) after the increase of length. The observed results first show a micellar growth (Table 1) and then a change of micellar symmetry as decanol is gradually added to the system. Taking into account the extended paraffin chain length (16.7 Å) and the polar shell thickness (4.6 Å), we should estimate the diameter of the SLS micelles to be 42.6 Å. However, the obtained Dmax values are greater than such a value, which indicates that the micellar aggregates might be elongated ellipsoids. The paraffinic anisotropies of the micelles were calculated according to eq 2. The obtained values of anisotropy increase from 1.40 ( 0.03 (at Md ) 0) to 1.59 ( 0.03 (at Md ) 0.18). The former value is

compatible with that obtained for the sample containing 9 wt % SLS in water (Md ) 0, ν ) 1.45).18,19 It is interesting to note that, using the same methodology, Glatter and co-workers21 have studied microemulsions and obtained the sequence of spherical, cylindrical, and planar structures for increasing temperatures in waterrich samples but for decreasing temperatures in oil-rich samples. IV. Discussion The first change in symmetry, from spherical to cylindrical, can be understood as a consequence of micellar growth induced by decanol addition.6,7,12 Decanol will be incorporated preferentially inside the spheroid micelles, enlarging their volume and size. The shape transformation from spheroid (prolate ellipsoid) to spherocylinder (SC) is predicted from bending energy considerations31 of the polar/apolar interface. The reason lies in the fact that ellipsoids have regions of variable and high curvature in the poles, while SC has fixed curvatures (1/3 in the hemispherical caps and 1/2 in the cylindrical body). The growth of a SC occurs without bending tension, and consequently, polydispersity is expected for a SC form. The bending energy of prolate ellipsoid and SC micelle forms has been explicitly calculated.31 It was demonstrated that for ν > 1.8, the SC shape is favored over the prolate shape for SLS micelles in the I phase. Since decanol prefers regions of lower curvature,11-13 mixed micelles may prefer the SC shape for even smaller anisotropies. (31) Taddei, G.; Amaral, L.Q. J. Phys. Chem. 1992, 96, 6102.

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Figure 4. Electron density distribution profiles generated by Decon, corresponding to the p j (r) functions of Figures 1-3. For Md ) 0.40, the Rpar value is taken as half of the third electron density level, as it coincides with the water electron density.

In our case, the micelles’ anisotropy at Md ) 0.20 is not known. However, as ν ≈ 1.6 at Md ) 0.18, and the indication that the micelles are growing with decanol

addition, we estimate that ν is close to 1.8 at Md ) 0.20. The shape transformation from cylinder to plane has been studied by Amaral et al.4,9,11 at the Nc f Nd transition

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correlates to x and to the micelle anisotropy ν through the following relationship:11

x ) u/(1 + u)

(4)

with

u)

Figure 5. Distance distribution functions of homogeneous particles simulated by ITP (s), along with the p(r), pc(r), and pt(r) obtained for the following samples (0): (a) homogeneous sphere and 10 wt % SLS/water, Md ) 0; (b) homogeneous cylinder and 10 wt % SLS/water, Md ) 0.33; (c) homogeneous lamella and 10 wt % SLS/water, Md ) 0.45.

in the SLS/water/decanol ternary system, which occurs at Md ) 0.38 for Mw ) 45.2 (26.25 wt % SLS in water). Such a result can be explained11 in terms of the bending energy of the SC and square-tablet (ST) forms, which depends on the decanol/SLS molar ratio in the spherocylinder body (assuming that only SLS is present in the curved caps), a variable referred to as x. The Md value

( )

(

v2 ν - 1 ν-1 1 + -1 ν - 1/3 Md v1 ν -1/3

)

(5)

where v1 and v2 are the paraffin chain volumes of surfactant and cosurfactant, respectively. The bending energy model developed for mixed micelles11 gives the equation for the SC-ST form transformation in terms of the variable x and the surfactant parameters of the amphiphile (p01) and cosurfactant (p02). From the known SC anisometry of 3 near the transition,32 the Nc f Nd transition occurs at x ) 0.64. Such an x value is in good agreement with the SC-ST form transformation predicted for p02 ) 1 (expected for decanol) and 0.5 e p01 e 0.6 (a reasonable value for SLS in the nematic liquidcrystalline phases). In the more dilute system studied (Mw ) 144.0), the change of symmetry from cylinder to lamella occurs at Md ) 0.40, a value only slightly different than that at which the Nc f Nd transition occurs (Md ) 0.38). From the above equations, correlating Md, ν, and x, the SC anisotropy should be about 3.4 for the same x value. A possible reason for a different p01 value in more dilute systems is a change in the amount of the hydration water. Therefore, we estimated such an amount as follows. The amount of hydration water (NH) in both cases (Mw ) 144.0 as determined here vs Mw ) 45.2 in ref 11) was calculated through eq 3 for Md ) 0 and 0.14, as these Md values have also been studied for the system containing 26.25 wt % SLS/water.6 The R values (R ) 0 for Md ) 0 and R ) 0.05 for Md ) 0.14) as well as the ν values (ν ) 2.4 for Md ) 0 and ν ) 3.0 for Md ) 0.14) for the concentrated system were taken from ref 6. It was found that NH ) 9.5 ( 1.0 for both systems and both Md values, which proves that, despite having much more water, the micelles effectively bind to water in the same amount in the present system as in the previous case. Therefore, we expect the same p01 value. This explains why the micelle form is sentitive to Md, but not to Mw. The competition between self-energy (single micelle curvature preference) and interaction (interaggregate effects) on the evolution of micellar shapes in ternary systems has been discussed by Noro and Gelbart.32 They show that at high total concentrations, the micellar shape is controlled not so much by the surfactant/cosurfactant ratio but by the relative efficiences of packing aggregates of different curvatures. Thus, the transition between longrange ordering hexagonal and lamellar phases can be predicted to occur with increased concentration. We stress, however, that such a model is unable to account for the small nematic islands that appear in these phase diagrams. The efficiency of packing aggregates of different curvature seems to be more related, in the case of small micelles, to the micelles’ capacity to grow. So, while SC micelles have anisotropies of ∼3 in Nc phases,33 their anisometry grows quickly in the Nd phase after the Nc f Nd transition. But the Nc f Nd transition itself is determined by the decanol/SLS molar ratio. (32) Noro, M. G.; Gelbart, W. M. J. Phys. Chem. 1997, 101, 8642. (33) Quist, P.O.; Halle, B.; Furo, O. J. Chem. Phys. 1992, 96, 3875.

Micellar Shape Transformation Induced by Decanol

In conclusion, our results indicate that the change of the micellar shape depends essentially on the decanol/ SLS molar ratio, and consequently, it is mainly ascribed to the intramicellar interactions, as formulated by the elastic bending theory of mixed micelles.11

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Acknowledgment. The authors thank PRONEX/ CNPq/MCT for financial support. C.V.T. thanks CAPES for the postgraduate fellowship. LA9912848